Results 1 to 10 of about 49,816 (162)

Monotonicity of the ratio of modified Bessel functions of the first kind with applications [PDF]

Journal of Inequalities and Applications, 2018
Let Wv(x)=xIv(x)/Iv+1(x) $W_{v} ( x ) =xI_{v} ( x ) /I_{v+1} ( x ) $ with Iv $I_{v}$ be the modified Bessel functions of the first kind of order v. In this paper, we prove the monotonicity of the function x↦(Wv(x)−p)2−(2v+2−p)2x2 $$ x\mapsto\frac{ ( W_{v}
Zhen-Hang Yang, Shen-Zhou Zheng
doaj   +7 more sources

Convexity of ratios of the modified Bessel functions of the first kind with applications. [PDF]

Rev Mat Complut, 2022
Let I ν x be the modified Bessel function of the first kind of order ν . Motivated by a conjecture on the convexity of the ratio W ν x = x I ν x / I ν + 1 x for ν > - 2 , using the monotonicity rules for a ratio of two power series and an elementary technique, we present fully the convexity of the functions W ν x , W ν x - x 2 / 2 ν + 4 ...
Yang ZH, Tian JF.
europepmc   +6 more sources

Arithmetic Means for a Class of Functions and the Modified Bessel Functions of the First Kind [PDF]

Mathematics, 2019
In the paper, by virtue of the residue theorem in the theory of complex functions, the authors establish several identities between arithmetic means for a class of functions and the modified Bessel functions of the first kind, present several identities ...
Feng Qi, Shao-Wen Yao, Bai-Ni Guo
doaj   +4 more sources

The logarithmic concavity of modified Bessel functions of the first kind and its related functions [PDF]

Advances in Difference Equations, 2019
This research demonstrates the log-convexity and log-concavity of the modified Bessel function of the first kind and the related functions. The method of coefficient is used to verify such properties.
Thanit Nanthanasub, Boriboon Novaprateep, Narongpol Wichailukkana   +2 more
doaj   +4 more sources

Geometric Nature of the Turánian of Modified Bessel Function of the First Kind [PDF]

Axioms
This work explores the geometric properties of the Turanian of the modified Bessel function of the first kind (TMBF). Using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starlikeness, convexity,
Samanway Sarkar, Dimiter Prodanov, Anish Kumar, Sourav Das   +3 more
doaj   +4 more sources

New Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean [PDF]

Mathematics, 2021
Let Ipx be the modified Bessel function of the first kind of order p. The upper and lower bounds in the form of simple rational functions about cosht and (sinht)/t for the function I0x are obtained.
Ling Zhu
doaj   +4 more sources

Fractional-Modified Bessel Function of the First Kind of Integer Order [PDF]

Mathematics, 2023
The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here, we generalize this MBF to include a fractional parameter, such that
Andrés Martín, Ernesto Estrada
  +9 more sources

Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications [PDF]

Mathematical Inequalities & Applications, 2017
Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ^{2}$ on $\left( 0,\infty \right) $.
Zhen-Hang Yang, Shenzhou Zheng
  +5 more sources

Double Integral involving the Product of the Bessel Function of the First Kind and Modified Bessel Function of the Second Kind: Derivation and Evaluation

European Journal of Pure and Applied Mathematics, 2022
A double integral whose kernel involves the Bessel functions Kv(xβ) and Jv(yα) is derived. This integral is expressed in terms of the Hurwitz-Lerch zeta function and evaluated for various values of the parameters involved. Some examples are evaluated and expressed in terms of fundamental constants. All the results in this work are new.
Robert Reynolds, A D Stauffer
openalex   +3 more sources

Redheffer type bounds for Bessel and modified Bessel functions of the\n first kind [PDF]

, 2017
In this paper our aim is to show some new inequalities of Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series.
Árpád Baricz, Khaled Mehrez
  +5 more sources